Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the chicken pieces and season with salt and black pepper. Cook until the chicken is browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms, bell pepper, and onion. Stir-fry for about 3-4 minutes until the vegetables are tender.
Add the minced garlic and ginger to the skillet, cooking for an additional 1 minute until fragrant.
In a small bowl, mix the soy sauce, oyster sauce (if using), cornstarch, and chicken broth until smooth. Pour this mixture into the skillet with the vegetables.
Return the cooked chicken to the skillet, stirring to combine everything. Cook for another 2-3 minutes until the sauce thickens and coats the chicken and vegetables.
Remove from heat and garnish with chopped green onions before serving.